(b) Fiber optic cable is available in 12 km lengths. How long will it take for a signal to travel that distance assuming that the speed of light in the cable is the same as in a vacuum?

Verified step by step guidance

1. Step 1: Understand the problem. We are asked to find the time it takes for a signal to travel a certain distance. We know the distance (12 km) and the speed of light in a vacuum, which is approximately 3.00 x 10^8 m/s.
2. Step 2: Convert the distance from kilometers to meters. 1 km is equal to 1000 m, so 12 km is equal to 12,000 m.
3. Step 3: Use the formula for time, which is distance divided by speed. In this case, the distance is 12,000 m and the speed is 3.00 x 10^8 m/s.
4. Step 4: Plug the values into the formula and solve for time. Remember to keep the units consistent - both the distance and speed should be in the same units (meters and meters per second, respectively).
5. Step 5: The result will be the time it takes for a signal to travel 12 km in a fiber optic cable, assuming the speed of light in the cable is the same as in a vacuum.

Key Concepts

Speed of Light

The speed of light in a vacuum is approximately 299,792 kilometers per second (km/s). This constant is fundamental in physics and is denoted by the symbol 'c'. In fiber optic cables, while the speed of light is reduced due to the medium, the question assumes it remains the same as in a vacuum, which simplifies calculations.

Distance and Time Relationship

The relationship between distance, speed, and time is described by the formula: distance = speed × time. This equation allows us to calculate the time it takes for a signal to travel a certain distance when the speed is known. Rearranging the formula gives time = distance/speed, which is essential for solving the problem presented.

Signal Propagation in Fiber Optics

In fiber optics, signals are transmitted as light pulses through thin strands of glass or plastic. The speed of light in these materials is typically slower than in a vacuum due to refraction, but the question specifies the speed as that in a vacuum. Understanding how light travels through different media is crucial for accurately determining signal travel times in practical applications.